Measuring forces between protein fibers by microscopy

The Sickle-Cell Fiber Revisited

Sickle cell disease is the consequence of a single point mutation on the surface of the β chains of the hemoglobin molecule leading to the formation of rigid polymers that disrupt circulation. It has long been established that the polymers are comprised of seven pairs of double strands that are twisted replicas of the double strands found in crystals. Here, we review several newer developments that elaborate on that simple model and provide deeper insights into the process.

Mesoscopic Adaptive Resolution Scheme toward Understanding of Interactions between Sickle Cell Fibers

Understanding of intracellular polymerization of sickle hemoglobin (HbS) and subsequent interaction with the membrane of a red blood cell (RBC) is important to predict the altered morphologies and mechanical properties of sickle RBCs in sickle cell anemia. However, modeling the integrated processes of HbS nucleation, polymerization, HbS fiber interaction, and subsequent distortion of RBCs is challenging as they occur at multispatial scales, ranging from nanometers to micrometers. To make progress toward simulating the integrated processes, we propose a hybrid HbS fiber model, which couples fine-grained and coarse-grained HbS fiber models through a mesoscopic adaptive resolution scheme (MARS). To this end, we apply a microscopic model to capture the dynamic process of polymerization of HbS fibers, while maintaining the mechanical properties of polymerized HbS fibers by the mesoscopic model, thus providing a means of bridging the subcellular and cellular phenomena in sickle cell disease. At the subcellular level, this model can simulate HbS polymerization with preexisting HbS nuclei. At the cellular level, if combined with RBC models, the generated HbS fibers could be applied to study the morphologies and membrane stiffening of sickle RBCs. One important feature of the MARS is that it can be easily employed in other particle-based multiscale simulations where a dynamic coarse-graining and force-blending method is required. As demonstrations, we first apply the hybrid HbS fiber model to simulate the interactions of two growing fibers and find that their final configurations depend on the orientation and interaction distance between two fibers, in good agreement with experimental observations. We also model the formation of fiber bundles and domains so that we explore the mechanism that causes fiber branching.

Dissecting the energies that stabilize sickle hemoglobin polymers

Sickle hemoglobin forms long, multistranded polymers that account for the pathophysiology of the disease. The molecules in these polymers make significant contacts along the polymer axis (i.e., axial contacts) as well as making diagonally directed contacts (i.e., lateral contacts). The axial contacts do not engage the mutant β6 Val and its nonmutant receptor region on an adjacent molecule, in contrast to the lateral contacts which do involve the mutation site. We have studied the association process by elastic light scattering measurements as a function of temperature, concentration, and primary and quaternary structure, employing an instrument of our own construction. Even well below the solubility for polymer formation, we find a difference between the association behavior of deoxy sickle hemoglobin molecules (HbS), which can polymerize at higher concentration, in comparison to COHbS, COHbA, or deoxygenated Hemoglobin A (HbA), none of which have the capacity to form polymers. The nonpolymerizable species are all quite similar to one another, and show much less association than deoxy HbS. We conclude that axial contacts are significantly weaker than the lateral ones. All the associations are entropically favored, and enthalpically disfavored, typical of hydrophobic interactions. For nonpolymerizable Hemoglobin, ΔH(o) was 35 ± 4 kcal/mol, and ΔS was 102.7 ± 0.5 cal/(mol-K). For deoxyHbS, ΔH(o) was 19 ± 2 kcal/mol, and ΔS was 56.9 ± 0.5 cal/(mol-K). The results are quantitatively consistent with the thermodynamics of polymer assembly, suggesting that the dimer contacts and polymer contacts are very similar, and they explain a previously documented significant anisotropy between bending and torsional moduli. Unexpectedly, the results also imply that a substantial fraction of the hemoglobin has associated into dimeric species at physiological conditions.

Modeling sickle hemoglobin fibers as one chain of coarse-grained particles

Sickle cell disease (SCD) is caused by a single point mutation in the beta-chain hemoglobin gene, resulting in the presence of abnormal hemoglobin S (HbS) in the patients' red blood cells (RBCs). In the deoxygenated state, the defective hemoglobin tetramers polymerize forming stiff fibers which distort the cell and contribute to changes in its biomechanical properties. Because the HbS fibers are essential in the formation of the sickle RBC, their material properties draw significant research interests. Here, a solvent-free coarse-grain molecular dynamics (CGMD) model is introduced to simulate single HbS fibers as a chain of particles. First, we show that the proposed model is able to efficiently simulate the mechanical behavior of single HbS fibers. Then, the zippering process between two HbS fibers is studied and the effect of depletion forces is investigated. Simulation results illustrate that depletion forces play a role comparable to direct fiber-fiber interaction via Van der Waals forces. This proposed model can greatly facilitate studies on HbS polymerization, fiber bundle and gel formation as well as interaction between HbS fiber bundles and the RBC membrane.

The mechanics of FtsZ fibers

Inhibition of the Fts family of proteins causes the growth of long filamentous cells, indicating that they play some role in cell division. FtsZ polymerizes into protofilaments and assembles into the Z-ring at the future site of the septum of cell division. We analyze the rigidity of GTP-bound FtsZ protofilaments by using cryoelectron microscopy to sample their bending fluctuations. We find that the FtsZ-GTP filament rigidity is κ=4.7±1.0×10(-27) Nm(2), with a corresponding thermal persistence length of l(p)=1.15±0.25μm, much higher than previous estimates. In conjunction with other model studies, our new higher estimate for FtsZ rigidity suggests that contraction of the Z-ring may generate sufficient force to facilitate cell division. The good agreement between the measured mode amplitudes and that predicted by equipartition of energy supports our use of a simple mechanical model for FtsZ fibers. The study also provides evidence that the fibers have no intrinsic global or local curvatures, such as might be caused by partial hydrolysis of the GTP.

Measuring forces between two single actin filaments during bundle formation

Bundles of filamentous actin are dominant cytoskeletal structures, which play a crucial role in various cellular processes. As yet quantifying the fundamental interaction between two individual actin filaments forming the smallest possible bundle has not been realized. Applying holographic optical tweezers integrated with a microfluidic platform, we were able to measure the forces between two actin filaments during bundle formation. Quantitative analysis yields forces up to 0.2 pN depending on the concentration of bundling agents.

Fiber depolymerization: fracture, fragments, vanishing times, and stochastics in sickle hemoglobin

The well-characterized rates, mechanisms, and stochastics of nucleation-dependent polymerization of deoxyhemoglobin S (HbS) are important in governing whether or not vaso-occlusive sickle cell crises will occur. The less well studied kinetics of depolymerization may also be important, for example in achieving full dissolution of polymers in the lungs, in resolution of crises and/or in minimizing gelation-induced cellular damage. We examine depolymerization by microscopic observations on depolymerizing HbS fibers, by Monte Carlo simulations and by analytical characterization of the mechanisms. We show that fibers fracture. Experimental scatter of rates is consistent with stochastic features of the analytical model and Monte Carlo results. We derive a model for the distribution of vanishing times and also show the distribution of fracture-dependent fiber fragment lengths and its time dependence. We describe differences between depolymerization of single fibers and bundles and propose models for bundle dissolution. Our basic model can be extended to dissolution of gels containing many fibers and is also applicable to other reversible linear polymers that dissolve by random fracture and end-depolymerization. Under the model, conditions in which residual HbS polymers exist and facilitate repolymerization and thus pathology can be defined; whereas for normal polymers requiring cyclic polymerization and depolymerization for function, conditions for rapid cycling due to residual aggregates can be identified.

Spontaneous emergence of sequence-dependent rosettelike folding of chromatin fiber

In the crowded environment of the eukaryotic nucleus, the presence of intrinsic structural defects is shown to predispose chromatin fiber to spontaneously form rosettelike structures. These multilooped patterns self-organize through entropy-driven clustering of sequence-induced fiber defects by depletive forces prior to any external factors coming into play. They provide an attractive description of replication foci that are observed in interphase mammalian nuclei as stable chromatin domains of autonomous DNA replication and gene expression. Experimental perspectives for in vivo visualization of rosettelike organization of the chromatin fiber via the clustering of recently identified putative replication initiation zones are discussed.

Force-induced desorption and unzipping of semiflexible polymers

The thermally assisted force-induced desorption of semiflexible polymers from an adhesive surface or the unzipping of two bound semiflexible polymers by a localized force are investigated. The phase diagram in the force-temperature plane is calculated both analytically and by Monte Carlo simulations. Force-induced desorption and unzipping of semiflexible polymers are first order phase transitions. A characteristic energy barrier for desorption is predicted, which scales with the square root of the polymer bending rigidity and governs the initial separation process before a plateau of constant separation force is reached. This leads to activated desorption and unzipping kinetics accessible in single molecule experiments.

Spatial persistence of angular correlations in amyloid fibrils

Using atomic force microscopy height maps, we resolve and quantify torsional fluctuations in one-dimensional amyloid fibril aggregates self-assembled from three different representative polypeptide systems. Furthermore, we show that angular correlation in these nanoscale structures is maintained over several microns, corresponding to many thousands of molecules along the fibril axis. We model disorder in the fibril in respect of both thermal fluctuations and structural defects, and determine quantitative values for the defect density, as well as the energy scales involved in the fundamental interactions stabilizing these generic structures.

Entropy-driven genome organization

DNA and RNA polymerases active on bacterial and human genomes in the crowded environment of a cell are modeled as beads spaced along a string. Aggregation of the large polymerizing complexes increases the entropy of the system through an increase in entropy of the many small crowding molecules; this occurs despite the entropic costs of looping the intervening DNA. Results of a quantitative cost/benefit analysis are consistent with observations that active polymerases cluster into replication and transcription "factories" in both pro- and eukaryotes. We conclude that the second law of thermodynamics acts through nonspecific entropic forces between engaged polymerases to drive the self-organization of genomes into loops containing several thousands (and sometimes millions) of basepairs.

Role of an S4-S5 linker lysine in the trafficking of the Ca(2+)-activated K(+) channels IK1 and SK3

We have investigated the role of the S4-S5 linker in the trafficking of the intermediate (human (h) IK1) and small (rat SK3) conductance K(+) channels using a combination of patch-clamp, protein biochemical, and immunofluorescence-based techniques. We demonstrate that a lysine residue (Lys(197)) located on the intracellular loop between the S4 and S5 domains is necessary for the correct trafficking of hIK1 to the plasma membrane. Mutation of this residue to either alanine or methionine precluded trafficking of the channel to the membrane, whereas the charge-conserving arginine mutation had no effect on channel localization or function. Immunofluorescence localization demonstrated that the K197A mutation resulted in a channel that was primarily retained in the endoplasmic reticulum, and this could not be rescued by incubation at 27 degrees C. Furthermore, immunoblot analysis revealed that the K197A mutation was overexpressed compared with wild-type hIK1 and that this was due to a greatly diminished rate of channel degradation. Co-immunoprecipitation studies demonstrated that the K197A mutation did not preclude multimer formation. Indeed, the K197A mutation dramatically suppressed expression of wild-type hIK1 at the cell surface. Finally, mutation of this conserved lysine in rat SK3 similarly resulted in a channel that failed to correctly traffic to the plasma membrane. These results are the first to demonstrate a critical role for the S4-S5 linker in the trafficking and/or function of IK and SK channels.